Thread: Good with integrals?

A 0.1-F capacitor measures 150V across it. At t=0, the capacitor is connected to a source that sends current i=16t/square root of (4t^2+9) amperes through the circuit. Find the voltage across the capacitor when t=2s.

I think you use this equation, but im not sure.
Vc=(1/C)xintegral of ixdt

You're completely right.

Basically, you know the Capacitance, and you're giving the function of current with respect to time. Since you can just Integrate your I function with respect to t.



Just use a simple u substitution so that

and

From there, you can just integrate the function as

and you will end up with the answer

Change your back into

Once you plug in your limits of 0 and 2 you will get

You know that so your final result should be